Node 27. Likelihood(MLE, MAP).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "opposite-carbon",
   "metadata": {},
   "source": [
    "## 확률 변수로서의 모델 파라미터"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "partial-legend",
   "metadata": {},
   "source": [
    "https://mml-book.github.io/ 를 참고하여 작성했다고 함"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "precise-sphere",
   "metadata": {},
   "source": [
    "$y=f(x)=ax+b$ ,  $a,b$ ∈ $R$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "broad-playlist",
   "metadata": {},
   "source": [
    "- 저 1차함수에서 a, b는 2차원 평면으로 나타낼 수 있는데,\n",
    "- 그 2차원 평면의 모든 점은 각각 하나의 함수에 대응한다고 볼 수 있다.\n",
    "- 그리고 그 2차원 평면은 `파마리터 공간(space)`라고 부를 수 있다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "concrete-dictionary",
   "metadata": {},
   "source": [
    "> 아래는 파라미터 공간에서 두 점 $a$, $b$를 뽑아 $y=ax+b$의 그래프를 그리는 코드입니다. 이론상으로는 실수 집합 전체에서 샘플링을 해야 하지만 코드로 구현하기가 불가능하고, 간단한 시각화를 위해 [-10, 10] 구간에서 샘플링했습니다.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "middle-opera",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "parameter_points = []\n",
    "fig1, axes1 = plt.subplots(2, 5, figsize=(10, 4))\n",
    "\n",
    "for ax in axes1.flatten():\n",
    "    # np.random.uniform: 정해진 구간에서 수를 무작위로 추출하여 반환합니다.\n",
    "    a, b = np.random.uniform(-10, 10, size=2)\n",
    "    a = round(a, 3)\n",
    "    b = round(b, 3)\n",
    "    parameter_points.append((a, b))\n",
    "\n",
    "    x = np.linspace(-10, 10, 50)\n",
    "    y = a*x + b\n",
    "    ax.plot(x, y)\n",
    "\n",
    "    ax.set_title('y='+str(a)+'x'+'{0:+.03f}'.format(b))\n",
    "    ax.set_xlim(-10, 10)\n",
    "    ax.set_ylim(-10, 10)\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "px, py = np.split(np.array(parameter_points), 2, axis=1)\n",
    "fig2 = plt.figure()\n",
    "axes2 = plt.gca()\n",
    "\n",
    "axes2.set_title('samples from parameter space')\n",
    "axes2.set_xlim(-10, 10)\n",
    "axes2.set_ylim(-10, 10)\n",
    "\n",
    "plt.scatter(px, py)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "excess-native",
   "metadata": {},
   "source": [
    "> - 아래 코드의 직관적 의미는\n",
    "> - a=1, b=0을 평균으로 하는 분포에서 a, b를 골라내면(즉, 절편이 0이고 기울기가 1이므로 다른 2차원 공간에서 y=x가 평균이 되게 하는)\n",
    "> - 대부분 저렇게 비슷하게 직선이 그어진다는 것"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "prime-novelty",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "parameter_points = []\n",
    "fig, axes1 = plt.subplots(2, 5, figsize=(10, 4))\n",
    "\n",
    "for ax in axes1.flatten():\n",
    "    # np.random.normal: 정규분포를 따르는 확률 변수의 랜덤한 값을 반환합니다.\n",
    "    a, b = np.random.normal(loc=[1, 0], scale=0.5)\n",
    "    a = round(a, 3)\n",
    "    b = round(b, 3)\n",
    "    parameter_points.append((a, b))\n",
    "\n",
    "    x = np.linspace(-10, 10, 50)\n",
    "    y = a*x + b\n",
    "    ax.plot(x, y)\n",
    "\n",
    "    ax.set_title('y='+str(a)+'x'+'{0:+.03f}'.format(b))\n",
    "    ax.set_xlim(-10, 10)\n",
    "    ax.set_ylim(-10, 10)\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "px, py = np.split(np.array(parameter_points), 2, axis=1)\n",
    "fig2 = plt.figure()\n",
    "axes2 = plt.gca()\n",
    "\n",
    "axes2.set_title('samples from parameter space')\n",
    "axes2.set_xlim(-10, 10)\n",
    "axes2.set_ylim(-10, 10)\n",
    "\n",
    "plt.scatter(px, py)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "hybrid-defendant",
   "metadata": {},
   "source": [
    "## posterior와 prior, likelihood 사이의 관계"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "moving-worker",
   "metadata": {},
   "source": [
    "- 베이지안 머신러닝 모델은 데이터를 통해 `파라미터 공간의 확률 분포`를 학습한다.\n",
    "- 파라미터를 고정된 변수로 놓는 것이 아닌 불확실성을 가진 `확률 변수`이고\n",
    "- 이 변수가 데이터를 관찰하면서 업데이트된다고 보는 것"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "going-redhead",
   "metadata": {},
   "source": [
    "### 사전 확률, 가능도, 사후 확률(prior, likelihood, posterior)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "forced-christopher",
   "metadata": {},
   "source": [
    "#### Prior\n",
    "- 데이터를 관찰하기 전 파라미터 공간에 주어진 확률 분포 $p(\\mathbf{\\theta})$를 **prior**(prior probability, **사전 확률**)이라고 한다.\n",
    "- 만약 prior 분포를 고정시킨다면, 주어진 파라미터 분포에 대해서 우리가 갖고 있는 데이터가 얼마나 '그럴듯한지' 계산할 수 있다. 이것을 나타내는 값이 **likelihood**(가능도, 우도).\n",
    "- 식으로는 $p(X=x∣θ)$\n",
    "- 즉, 파라미터의 분포 $p(\\mathbf{\\theta})$가 정해졌을 때 xx라는 데이터가 관찰될 확률\n",
    "- 결국 우리가 구하고 싶은 것은 모델의 파라미터 $\\mathbf{\\theta}$의 값이고, 데이터는 이미 알고 있는 고정된 값이니까\n",
    "- likelihood가 높다는 것은 곧 우리가 지정한 파라미터 조건에서 데이터가 관찰될 확률이 높다는 것이고, 데이터의 분포를 모델이 잘 표현하는 것이라고 생각할 수 있다.\n",
    "- 그래서 데이터들의 likelihood 값을 최대화하는 방향으로 모델을 학습시키는 방법을 **최대 가능도 추정(maximum likelihood estimation, MLE)**이라고 한다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "immediate-roman",
   "metadata": {},
   "source": [
    "#### Posterior\n",
    "- 반대로, 데이터 집합 $X$가 주어졌을 때 파라미터 $\\mathbf{\\theta}$의 분포 $p(\\mathbf{\\theta}|X)$를 생각해 볼 수 있다.\n",
    "- 이 값을 '데이터를 관찰한 후 계산되는 확률'이라는 뜻에서 **posterior(posterior probability, 사후 확률)** 라고 부른다.\n",
    "- 생각해 보면 이게 우리한테 필요한 값인데, 데이터 포인트의 개수는 유한하기 때문에 데이터가 따르는 확률 분포 $p(X)$는 우리가 정확하게 알 수 없다.\n",
    "- 애초에 머신러닝의 목표가 $p(X)$를 직접 구할 수가 없으니까 모델 파라미터 $\\mathbf{\\theta}$를 조절해가며 간접적으로 근사하는 것이었음.\n",
    "- 그래서 posterior를 직접 계산해서 최적의 $\\mathbf{\\theta}$ 값을 찾는 것이 아니라, **prior와 likelihood에 관한 식**으로 변형한 다음, 그 식을 최대화하는 파라미터 $\\mathbf{\\theta}$를 찾는다.\n",
    "- 이렇게 posterior를 최대화하는 방향으로 모델을 학습시키는 방법을 **최대 사후 확률 추정(maximum a posteriori estimation, MAP)** 이라고 함"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "satisfactory-better",
   "metadata": {},
   "source": [
    "## likelihood와 머신러닝"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "multiple-pierce",
   "metadata": {},
   "source": [
    "- 머신러닝 모델은 어디까지나 한정된 파라미터로 데이터의 실제 분포를 근사하는 역할을 하기 때문에, 어떤 데이터가 들어와도 100%의 정확도를 내는 모델을 만들기는 불가능함\n",
    "- 그래서 모델이 입력 데이터로부터 예측한 출력 데이터(prediction)와 우리가 알고 있는 데이터의 실제 값(label) 사이에는 오차가 생기게 되는데,\n",
    "- 이 오차를 우리에게 관찰되는 데이터에는 이미 노이즈가 섞여있어서 발생한다고 해석한다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "visible-matrix",
   "metadata": {},
   "source": [
    "- **likelihood**는 파라미터 분포가 주어졌을 때 특정 데이터가 관찰될 확률 $p(X=x|\\mathbf{\\theta})$를 나타냄\n",
    "- 지도 학습의 예시에서는, 파라미터 분포 $\\mathbf{\\theta}$와 입력 데이터 $\\mathbf{x}_n$ 이 주어졌을 때 라벨 $y_n$ 을 예측하는 문제가 됨. \n",
    "- 입력 데이터의 집합을 $X$, 라벨들의 집합을 $Y$라고 할 때, **likelihood**는 파라미터와 입력 데이터가 주어졌을 때 출력값(라벨)의 확률 분포, 즉 $p(Y|\\mathbf{\\theta}, X)$가 된다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "respected-cache",
   "metadata": {},
   "source": [
    "- 데이터셋 전체의 likelihood 대신 데이터 하나의 likelihood $p(y_n|\\mathbf{\\theta}$, $\\mathbf{x}_n)$\n",
    " )을 생각해 보자.\n",
    "- 출력값의 분포를 어떻게 생각할 수 있을까? 모델을 선형 모델 $y=\\mathbf{\\theta}^\\top\\mathbf{x}$로 잡았을 때, 출력값의 분포는 모델의 예측값 $\\mathbf{\\theta}^\\top\\mathbf{x}_n$에다가 노이즈의 분포를 더한 값이 될 것이다.\n",
    "- 노이즈 분포를 `평균이 0`이고 표준편차가 $\\sigma$인 정규분포로 가정한다면, 출력값의 분포는 평균이 $\\mathbf{\\theta}^\\top\\mathbf{x}_n$ 이고 표준편차가 $\\sigma$인 정규분포가 된다.\n",
    "![](https://images.velog.io/images/moondeokjong/post/746cb91d-1858-4cda-98ee-41685eb51834/Screenshot%202022-02-16%20at%2011.50.30%20AM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "czech-utilization",
   "metadata": {},
   "source": [
    "- xy 평면 위에 모델에 해당하는 빨간색 직선이 있다. 출력값의 분포를 나타내기 위해서 $p(y)$ 좌표축을 추가했고,\n",
    "- 입력 데이터가 $\\mathbf{x}_n$ 일 때 모델의 예측값은 $\\mathbf{\\theta}^\\top\\mathbf{x}_n$ 이고, 출력값의 분포 $p(y_n|\\mathbf{\\theta}, \\mathbf{x}_n)$ 은 노란색으로 표시한 정규분포 그래프가 된다.\n",
    "\n",
    " ![](https://images.velog.io/images/moondeokjong/post/4effa677-b126-4ec4-91ea-c55c66ab869a/Screenshot%202022-02-16%20at%2011.52.08%20AM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fantastic-election",
   "metadata": {},
   "source": [
    "## likelihood 감 잡기"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "champion-service",
   "metadata": {},
   "source": [
    "- 아래는 5개의 데이터 포인트를 생성하고 그것에 노이즈를 입힌 것을 좌표평면에 나타냄"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "exempt-admission",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(321)\n",
    "\n",
    "input_data = np.linspace(-2, 2, 5)\n",
    "label = input_data + 1 + np.random.normal(0, 1, size=5)\n",
    "\n",
    "plt.scatter(input_data, label)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "brazilian-findings",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2., -1.,  0.,  1.,  2.])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "working-albania",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.82748053,  1.63548253,  1.0373364 ,  1.11585031,  1.85680774])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "label"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "lined-quantity",
   "metadata": {},
   "source": [
    "- 위의 식에서 **1차함수 식**을 바꾸면 데이터포인트 5개의 likelihood가 어떻게 바뀌는지 보는 것으로 해석할 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "refined-paper",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "label2 = input_data * 2 + np.random.normal(0, 1, size=5)\n",
    "\n",
    "plt.scatter(input_data, label2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "convinced-money",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "label3 = input_data * 3 + np.random.normal(0, 1, size=5)\n",
    "\n",
    "plt.scatter(input_data, label3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "juvenile-questionnaire",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "label4 = input_data -3 + np.random.normal(0, 1, size=5)\n",
    "\n",
    "plt.scatter(input_data, label4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sharing-baghdad",
   "metadata": {},
   "source": [
    "#### 노이즈 분포의 표준편차는 데이터의 실제 분포와 관련된 값이라 우리가 알 수 없다\n",
    "#### 그러나 MLE를 사용하면 표준편차를 알지 못해도 최적의 파라미터 값을 찾을 수 있다.\n",
    "\n",
    "- 한번 likelihood가 어떻게 바뀌는지 봐보자\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "great-feedback",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# model: y = ax + b\n",
    "# a, b 값을 바꾸면서 실행해보세요\n",
    "#-------------------------------#\n",
    "a = 1\n",
    "b = 1\n",
    "#-------------------------------#\n",
    "\n",
    "# 모델 예측값\n",
    "model_output = a*input_data + b\n",
    "likelihood = []\n",
    "\n",
    "# x: 입력데이터, y: 데이터라벨\n",
    "# 예측값과 라벨의 차이를 제곱해 exp에 사용\n",
    "for x, y, output in zip(input_data, label, model_output):\n",
    "    likelihood.append(1/(math.sqrt(2*math.pi*0.1*0.1))*math.exp(-pow(y-output,2)/(2*0.1*0.1)))\n",
    "\n",
    "model_x = np.linspace(-2, 2, 50)\n",
    "model_y = a*model_x + b\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(input_data, label)\n",
    "ax.plot(model_x, model_y)\n",
    "\n",
    "for i, text in enumerate(likelihood):\n",
    "    ax.annotate('%.3e'%text, (input_data[i], label[i]))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "devoted-expression",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# model: y = ax + b\n",
    "# a, b 값을 바꾸면서 실행해보세요\n",
    "#-------------------------------#\n",
    "a = 3\n",
    "b = 1\n",
    "#-------------------------------#\n",
    "\n",
    "# 모델 예측값\n",
    "model_output = a*input_data + b\n",
    "likelihood = []\n",
    "\n",
    "# x: 입력데이터, y: 데이터라벨\n",
    "# 예측값과 라벨의 차이를 제곱해 exp에 사용\n",
    "for x, y, output in zip(input_data, label, model_output):\n",
    "    likelihood.append(1/(math.sqrt(2*math.pi*0.1*0.1))*math.exp(-pow(y-output,2)/(2*0.1*0.1)))\n",
    "\n",
    "model_x = np.linspace(-2, 2, 50)\n",
    "model_y = a*model_x + b\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(input_data, label)\n",
    "ax.plot(model_x, model_y)\n",
    "\n",
    "for i, text in enumerate(likelihood):\n",
    "    ax.annotate('%.3e'%text, (input_data[i], label[i]))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fluid-fifth",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# model: y = ax + b\n",
    "# a, b 값을 바꾸면서 실행해보세요\n",
    "#-------------------------------#\n",
    "a = 3\n",
    "b = 10\n",
    "#-------------------------------#\n",
    "\n",
    "# 모델 예측값\n",
    "model_output = a*input_data + b\n",
    "likelihood = []\n",
    "\n",
    "# x: 입력데이터, y: 데이터라벨\n",
    "# 예측값과 라벨의 차이를 제곱해 exp에 사용\n",
    "for x, y, output in zip(input_data, label, model_output):\n",
    "    likelihood.append(1/(math.sqrt(2*math.pi*0.1*0.1))*math.exp(-pow(y-output,2)/(2*0.1*0.1)))\n",
    "\n",
    "model_x = np.linspace(-2, 2, 50)\n",
    "model_y = a*model_x + b\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(input_data, label)\n",
    "ax.plot(model_x, model_y)\n",
    "\n",
    "for i, text in enumerate(likelihood):\n",
    "    ax.annotate('%.3e'%text, (input_data[i], label[i]))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "signed-devil",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# model: y = ax + b\n",
    "# a, b 값을 바꾸면서 실행해보세요\n",
    "#-------------------------------#\n",
    "a = 10\n",
    "b = 0 \n",
    "#-------------------------------#\n",
    "\n",
    "# 모델 예측값\n",
    "model_output = a*input_data + b\n",
    "likelihood = []\n",
    "\n",
    "# x: 입력데이터, y: 데이터라벨\n",
    "# 예측값과 라벨의 차이를 제곱해 exp에 사용\n",
    "for x, y, output in zip(input_data, label, model_output):\n",
    "    likelihood.append(1/(math.sqrt(2*math.pi*0.1*0.1))*math.exp(-pow(y-output,2)/(2*0.1*0.1)))\n",
    "\n",
    "model_x = np.linspace(-2, 2, 50)\n",
    "model_y = a*model_x + b\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(input_data, label)\n",
    "ax.plot(model_x, model_y)\n",
    "\n",
    "for i, text in enumerate(likelihood):\n",
    "    ax.annotate('%.3e'%text, (input_data[i], label[i]))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "lasting-victim",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# model: y = ax + b\n",
    "# a, b 값을 바꾸면서 실행해보세요\n",
    "#-------------------------------#\n",
    "a = 0.1\n",
    "b = 0 \n",
    "#-------------------------------#\n",
    "\n",
    "# 모델 예측값\n",
    "model_output = a*input_data + b\n",
    "likelihood = []\n",
    "\n",
    "# x: 입력데이터, y: 데이터라벨\n",
    "# 예측값과 라벨의 차이를 제곱해 exp에 사용\n",
    "for x, y, output in zip(input_data, label, model_output):\n",
    "    likelihood.append(1/(math.sqrt(2*math.pi*0.1*0.1))*math.exp(-pow(y-output,2)/(2*0.1*0.1)))\n",
    "\n",
    "model_x = np.linspace(-2, 2, 50)\n",
    "model_y = a*model_x + b\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.scatter(input_data, label)\n",
    "ax.plot(model_x, model_y)\n",
    "\n",
    "for i, text in enumerate(likelihood):\n",
    "    ax.annotate('%.3e'%text, (input_data[i], label[i]))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "blocked-education",
   "metadata": {},
   "source": [
    "### likelihood가 왜 중요한가?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "western-arrival",
   "metadata": {},
   "source": [
    "- 위 예제에서 보이듯이, 데이터 포인트가 모델 함수에서 멀어질수록 데이터의 likelihood는 기하급수적으로 감소한다.\n",
    "- likelihood를 구하는 식을 보면 모델 예측값과 데이터 라벨의 차이를 제곱해서 exponential 위에 올려놓은 것을 확인할 수 있다.\n",
    "- 그래서 예측값과 라벨의 차이가 조금만 벌어져도 likelihood 값은 민감하게 반응한다.\n",
    "- #### 머신러닝의 목표가 데이터 포인트들을 최대한 잘 표현하는 모델을 찾는 것이었다는 사실을 생각하면, 결국 데이터 포인트들의 likelihood 값을 크게 하는 모델을 찾는 것이 목표가 된다.\n",
    "- #### 바로 그렇게 데이터의 likelihood 값을 최대화하는 모델 파라미터를 찾는 방법이 최대 가능도 추론(maximum likelihood estimation, MLE)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "guilty-three",
   "metadata": {},
   "source": [
    "## MLE: 최대 가능도 추론"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "thousand-coalition",
   "metadata": {},
   "source": [
    "### 데이터셋 전체의 likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "opening-intervention",
   "metadata": {},
   "source": [
    "- 좋은 머신러닝 모델은 하나의 데이터에 대해서만 likelihood가 큰 모델이 아니라, 데이터셋에 있는 모든 데이터 포인트의 likelihood 값을 크게 만드는 모델\n",
    "- 데이터셋 전체의 likelihood는 어떻게 구하면 좋을까?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "existing-privacy",
   "metadata": {},
   "source": [
    "- 우리가 가지고 있는 데이터 포인트 $(\\mathbf{x}_1, y_1)$, $\\dots$, $(\\mathbf{x}_n, y_n)$은 서로 독립이고(independent) 같은 확률 분포를 따른다고(identically distributed) 가정\n",
    "- 이 조건을 independent and identically distributed, 줄여서 i.i.d.라고 부르는데, **머신러닝 문제에서 꼭 필요한 전제조건** 이다.\n",
    "- 데이터 포인트들이 서로 독립이므로, 데이터셋 전체의 likelihood $p(Y|\\mathbf{\\theta}, X)$는 데이터 포인트 각각의 likelihood를 모두 곱한 값과 같다.\n",
    "\n",
    "![](https://images.velog.io/images/moondeokjong/post/684e391b-c7eb-431b-9098-9637f96c651c/Screenshot%202022-02-16%20at%2012.16.18%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "obvious-interstate",
   "metadata": {},
   "source": [
    "- MLE를 실제로 적용할 때는 likelihood 대신 log likelihood를 최대화하는 파라미터를 구한다다. \n",
    "- 왜냐하면 데이터셋의 likelihood가 데이터 포인트 각각의 likelihood를 곱한 형태인데, 로그를 씌우면 곱셈 연산이 덧셈 연산으로 바뀌면서 미분 계산이 편리해져서이다.\n",
    "- 또한 로그 함수는 단조 증가(monotonically increasing)하므로 likelihood를 최대화하는 파라미터와 log likelihood를 최대화하는 파라미터 값이 같아서 학습 결과에 영향을 주지 않는다.\n",
    "\n",
    "> - 구현 측면에서 보면, 앞 스텝의 예제에서 보셨듯이 likelihood 값은 0에 가까운 수로 많이 계산된다. \n",
    "> - 이 수들을 곱하다 보면 CPU가 계산할 수 있는 범위를 넘어서는 언더플로우가 발생할 가능성이 있다.\n",
    "> - 그러나 likelihood 값에 로그를 씌우면 이런 문제를 예방할 수 있다.\n",
    "\n",
    "![](https://images.velog.io/images/moondeokjong/post/144e5553-f565-4061-96db-8bd996ecda8a/Screenshot%202022-02-16%20at%2012.28.33%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "important-louis",
   "metadata": {},
   "source": [
    "likelihood를 최대화하는 파라미터를 $\\mathbf{\\theta}_{ML}$(ML: maximum likelihood)이라고 하면\n",
    "\n",
    "![](https://images.velog.io/images/moondeokjong/post/8a785a50-7272-4eee-b47b-5e279891b444/Screenshot%202022-02-16%20at%2012.29.16%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "choice-preference",
   "metadata": {},
   "source": [
    "- θ와 관계없는 부분을 빼고 식을 정리하면 다음과 같다.\n",
    "- 손실 함수를 최소화하는 관점에서, log likelihood를 최대화하는 대신 negative log likelihood $(-\\log p(Y|\\mathbf{\\theta}, X))$를 최소화하는 식으로 나타내기도 한다\n",
    "\n",
    "![](https://images.velog.io/images/moondeokjong/post/fcfbede5-b222-4282-a9a8-e44e75d415b1/Screenshot%202022-02-16%20at%2012.31.07%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pending-weight",
   "metadata": {},
   "source": [
    "- 최소제곱법(least square)의 식과 같은 것을 확인할 수 있다. \n",
    "- 최소제곱법은 선형 모델에서 노이즈의 분포가 $\\mathcal{N}(0,\\sigma^2)$라고 가정할 때 **negative log likelihood**를 최소화하는 파라미터 값을 찾는 것과 본질적으로 같다.\n",
    "- 우리가 최소화해야 할 식을 $\\mathbf{\\theta}$에 대한 함수 $\\mathcal{L}(\\mathbf{\\theta})$로 놓으면\n",
    "![](https://images.velog.io/images/moondeokjong/post/85beac4c-4999-47d7-9f58-8bc3d819652d/Screenshot%202022-02-16%20at%2012.32.47%20PM.png)\n",
    "- #### L(θ)를 최소화하는 $\\mathbf{\\theta}$의 값은 $\\mathcal{L}(\\mathbf{\\theta})$를 $\\mathbf{\\theta}$θ에 대해 미분한 식을 0으로 만드는 $\\mathbf{\\theta}$의 값과 같다.\n",
    "- 물론 일반적으로는 도함수의 부호 변화나 local minimum 여부 등을 모두 따져야 하지만, \n",
    "- $\\mathcal{L}(\\mathbf{\\theta})$는 $\\mathbf{\\theta}$에 대한 이차식이므로 유일한 최솟값을 가진다. \n",
    "- 따라서 도함수를 0으로 만드는 $\\mathbf{\\theta}$값을 찾는 것으로도 충분하다.\n",
    "\n",
    "![](https://images.velog.io/images/moondeokjong/post/e5899ae7-b498-49c3-af61-2b9f8debf035/Screenshot%202022-02-16%20at%2012.35.09%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compatible-craps",
   "metadata": {},
   "source": [
    "### maximum 'log' likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "agreed-procedure",
   "metadata": {},
   "source": [
    "![](https://images.velog.io/images/moondeokjong/post/ce2d431c-f09a-415a-85bf-e899bb5d8010/Screenshot%202022-02-16%20at%2012.37.03%20PM.png)\n",
    "![](https://images.velog.io/images/moondeokjong/post/f45b3360-a40e-4436-ab2e-ca6ccae2daf9/Screenshot%202022-02-16%20at%2012.37.09%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "north-allowance",
   "metadata": {},
   "source": [
    "## MLE 최적해 구하기"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "extra-signature",
   "metadata": {},
   "source": [
    "### 데이터셋 생성\n",
    "\n",
    "- MLE를 이용해 최적의 파라미터를 찾아보고 데이터셋의 likelihood도 계산해 보자. \n",
    "- 아래 코드는 $y=x+1$ 함수를 기준으로 랜덤한 노이즈를 섞어서 데이터 포인트 20개를 생성하고 시각화하는 코드.\n",
    "- 데이터 생성 단계에서 지정한 노이즈의 분포는 평균이 0이고 표준편차가 0.5인 정규분포."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "brilliant-short",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(0)\n",
    "num_samples = 20\n",
    "\n",
    "input_data = np.linspace(-2, 2, num_samples)\n",
    "labels = input_data + 1 + np.random.normal(0, 0.5, size=num_samples)\n",
    "\n",
    "plt.scatter(input_data, labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "different-sheet",
   "metadata": {},
   "source": [
    "### likelihood와 파라미터 계산"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "scenic-transition",
   "metadata": {},
   "source": [
    "- 데이터를 생성할 때는 노이즈 분포의 표준편차를 0.5로 정했지만 데이터를 관찰하고 모델을 설계하는 입장에서는 노이즈의 원래 표준편차를 알 수 없다. \n",
    "- 노이즈의 표준편차를 0.1로 가정했다고 하면, likelihood와 negative log likelihood는 다음과 같이 계산된다.\n",
    "![](https://images.velog.io/images/moondeokjong/post/a01860ec-4c6b-4f6e-90a8-8e3d633ebc77/Screenshot%202022-02-16%20at%2012.40.13%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abandoned-female",
   "metadata": {},
   "source": [
    "- 구현에서 주의해야 할 부분은, 입력 데이터가 실수 스칼라 값을 갖는 것처럼 보이지만 실제로는 변수 $x$와 상수항이 묶인 2차원 열벡터로 표현된다는 것\n",
    "![](https://images.velog.io/images/moondeokjong/post/e4d250fc-7f59-4868-8bdf-2ebad2b5e3b5/Screenshot%202022-02-16%20at%2012.41.17%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "clean-reporter",
   "metadata": {},
   "source": [
    "- MLE의 최적 파라미터 $\\mathbf{\\theta}_{ML}$ 은 다음과 같이 계산된다.\n",
    "![](https://images.velog.io/images/moondeokjong/post/311f16eb-8a08-42da-98cc-d8207db8129a/Screenshot%202022-02-16%20at%2012.44.52%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "distinguished-lancaster",
   "metadata": {},
   "source": [
    "- 위의 식을 코드로 구현해서 구해보면,\n",
    "- 아래 코드로 구한 최적의 모델은 $y=0.8578x+1.2847$이다. \n",
    "- 데이터 포인트들이 $y=x+1$ 함수로부터 생성된 것을 생각하면 꽤 가까운 결과가 나왔다.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "plain-andrew",
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood(labels, preds):\n",
    "    result = 1/(np.sqrt(2*math.pi*0.1*0.1))*np.exp(-np.power(labels-preds,2)/(2*0.1*0.1))\n",
    "    \n",
    "    return np.prod(result)\n",
    "\n",
    "def neg_log_likelihood(labels, preds):\n",
    "    const_term = len(labels)*math.log(1/math.sqrt(2*math.pi*0.1*0.1))\n",
    "\n",
    "    return (-1)*(const_term + 1/(2*0.1*0.1)*np.sum(-np.power(labels-preds,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "former-pavilion",
   "metadata": {},
   "source": [
    "> #### 신기한 게 optimization 같이 여러번 반복해서 구한 게 아님에도 저 수식 하나로 파라미터가 구해진다.\n",
    "> #### 아마 Loss 함수의 미분 값이 0이 되는 식으로 이미 방정식을 만들어놓아서 그런 것 같다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "obvious-action",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope: 0.8578 bias: 1.2847\n",
      "likelihood: 2.9724e-54\n",
      "negative log likelihood: 1.2325e+02\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# X: 20x2 matrix, y: 20x1 matrix\n",
    "# input_data 리스트를 column vector로 바꾼 다음 np.append 함수로 상수항을 추가합니다.\n",
    "X = np.append(input_data.reshape((-1, 1)), np.ones((num_samples, 1)), axis=1)\n",
    "y = labels\n",
    "\n",
    "theta_1, theta_0 = np.dot(np.dot(np.linalg.inv(np.dot(X.T, X)), X.T), y)\n",
    "\n",
    "print('slope: '+'%.4f'%theta_1+' bias: '+'%.4f'%theta_0)\n",
    "\n",
    "predictions = theta_1 * input_data + theta_0\n",
    "print('likelihood: '+'%.4e'%likelihood(labels, predictions))\n",
    "print('negative log likelihood: '+'%.4e'%neg_log_likelihood(labels, predictions))\n",
    "\n",
    "model_x = np.linspace(-2, 2, 50)\n",
    "model_y = theta_1 * model_x + theta_0\n",
    "\n",
    "plt.scatter(input_data, labels)\n",
    "plt.plot(model_x, model_y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "veterinary-measurement",
   "metadata": {},
   "source": [
    "-----------\n",
    "-----------\n",
    "-----------\n",
    "-----------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "premium-excess",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.        ,  1.        ],\n",
       "       [-1.78947368,  1.        ],\n",
       "       [-1.57894737,  1.        ],\n",
       "       [-1.36842105,  1.        ],\n",
       "       [-1.15789474,  1.        ],\n",
       "       [-0.94736842,  1.        ],\n",
       "       [-0.73684211,  1.        ],\n",
       "       [-0.52631579,  1.        ],\n",
       "       [-0.31578947,  1.        ],\n",
       "       [-0.10526316,  1.        ],\n",
       "       [ 0.10526316,  1.        ],\n",
       "       [ 0.31578947,  1.        ],\n",
       "       [ 0.52631579,  1.        ],\n",
       "       [ 0.73684211,  1.        ],\n",
       "       [ 0.94736842,  1.        ],\n",
       "       [ 1.15789474,  1.        ],\n",
       "       [ 1.36842105,  1.        ],\n",
       "       [ 1.57894737,  1.        ],\n",
       "       [ 1.78947368,  1.        ],\n",
       "       [ 2.        ,  1.        ]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "parallel-banner",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.        ,  1.        ,  1.        ,  1.        ],\n",
       "       [-1.78947368,  1.        ,  1.        ,  1.        ],\n",
       "       [-1.57894737,  1.        ,  1.        ,  1.        ],\n",
       "       [-1.36842105,  1.        ,  1.        ,  1.        ],\n",
       "       [-1.15789474,  1.        ,  1.        ,  1.        ],\n",
       "       [-0.94736842,  1.        ,  1.        ,  1.        ],\n",
       "       [-0.73684211,  1.        ,  1.        ,  1.        ],\n",
       "       [-0.52631579,  1.        ,  1.        ,  1.        ],\n",
       "       [-0.31578947,  1.        ,  1.        ,  1.        ],\n",
       "       [-0.10526316,  1.        ,  1.        ,  1.        ],\n",
       "       [ 0.10526316,  1.        ,  1.        ,  1.        ],\n",
       "       [ 0.31578947,  1.        ,  1.        ,  1.        ],\n",
       "       [ 0.52631579,  1.        ,  1.        ,  1.        ],\n",
       "       [ 0.73684211,  1.        ,  1.        ,  1.        ],\n",
       "       [ 0.94736842,  1.        ,  1.        ,  1.        ],\n",
       "       [ 1.15789474,  1.        ,  1.        ,  1.        ],\n",
       "       [ 1.36842105,  1.        ,  1.        ,  1.        ],\n",
       "       [ 1.57894737,  1.        ,  1.        ,  1.        ],\n",
       "       [ 1.78947368,  1.        ,  1.        ,  1.        ],\n",
       "       [ 2.        ,  1.        ,  1.        ,  1.        ]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.append(X, np.ones(X.shape), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "willing-constraint",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.        ],\n",
       "       [-1.78947368],\n",
       "       [-1.57894737],\n",
       "       [-1.36842105],\n",
       "       [-1.15789474],\n",
       "       [-0.94736842],\n",
       "       [-0.73684211],\n",
       "       [-0.52631579],\n",
       "       [-0.31578947],\n",
       "       [-0.10526316],\n",
       "       [ 0.10526316],\n",
       "       [ 0.31578947],\n",
       "       [ 0.52631579],\n",
       "       [ 0.73684211],\n",
       "       [ 0.94736842],\n",
       "       [ 1.15789474],\n",
       "       [ 1.36842105],\n",
       "       [ 1.57894737],\n",
       "       [ 1.78947368],\n",
       "       [ 2.        ]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "input_data.reshape((-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "retired-sigma",
   "metadata": {},
   "source": [
    "-----------\n",
    "-----------\n",
    "-----------\n",
    "-----------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "severe-ethernet",
   "metadata": {},
   "source": [
    "## MAP: 최대 사후 확률 추정"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "continental-delay",
   "metadata": {},
   "source": [
    "### prior 분포의 등장"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "clean-campus",
   "metadata": {},
   "source": [
    "- 선형 회귀 문제에서 MLE로 구한 최적 파라미터 식을 다시 살펴보자. $\\mathbf{\\theta}_{ML} = (X^\\top X)^{-1}X^\\top\\mathbf{y}$\n",
    "- $X$는 데이터셋 행렬이고, $\\mathbf{y}$는 라벨들을 모아놓은 벡터. \n",
    "- 이 식에서 알 수 있는 것은, MLE의 최적해는 **오로지 관측된 데이터 값에만 의존 한다는 사실**이다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "weighted-labor",
   "metadata": {},
   "source": [
    "- 물론 이런 접근법은 계산이 비교적 간단하다는 장점이 있지만, \n",
    "- 관측된 데이터에 노이즈가 많이 섞여 있는 경우, 이상치(outlier) 데이터가 존재하는 경우에는 모델의 안정성이 떨어진다는 단점도 있다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "casual-validation",
   "metadata": {},
   "source": [
    "- MAP는 데이터셋이 주어졌을 때 파라미터의 분포, 즉 $p(\\mathbf{\\theta}|X)$에서 확률 값을 최대화하는 파라미터 $\\mathbf{\\theta}$를 찾는다. \n",
    "- 직관적으로 이야기하면 '이런 데이터가 있을 때 파라미터의 값이 무엇일 확률이 제일 높은가?'를 푼다."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dietary-timber",
   "metadata": {},
   "source": [
    "- 지도 학습의 경우 posterior는 $p(\\mathbf{\\theta}|X,Y)$로 나타낼 수 있다. \n",
    "- 이 식을 prior $p(\\mathbf{\\theta})$와 likelihood $p(Y|\\mathbf{\\theta},X)$에 관한 식으로 변형하면 다음과 같다.\n",
    "\n",
    "![](https://images.velog.io/images/moondeokjong/post/2e7e348c-f12b-4498-b03a-eb7d38288af3/Screenshot%202022-02-16%20at%202.20.37%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "different-wrestling",
   "metadata": {},
   "source": [
    "- prior 분포 $p(\\mathbf{\\theta})$는 관찰된 데이터가 없을 때 파라미터 공간에 주어진 확률 분포이다. \n",
    "- $p(\\mathbf{\\theta}=\\theta_0)$ 값을 크게 만드는 파라미터 $\\mathbf{\\theta}_0$을 '그럴듯한' 파라미터로 생각하는 것이다.\n",
    "- 여기에서는 $p(\\mathbf{\\theta})$를 평균이 $(0,0)$이고 공분산 $\\Sigma=\\alpha^2\\mathbf{I}$인 정규분포로 정의 ($\\Sigma=\\alpha^2\\mathbf{I}$이므로 $|\\Sigma|=\\alpha^4$, $\\Sigma^{-1}=(1/\\alpha^2)\\mathbf{I}$\n",
    "\n",
    " ![](https://images.velog.io/images/moondeokjong/post/f4bbfb8c-5ddd-4cbf-9716-ee81abb9413b/Screenshot%202022-02-16%20at%202.54.08%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "flexible-arbor",
   "metadata": {},
   "source": [
    "- MLE에서 negative log likelihood를 최소화했던 것과 같이, MAP에서도 실제로는 posterior를 최대화하는 파라미터 대신 negative log posterior를 최소화하는 파라미터 값을 구한다.\n",
    "- 식을 정리하면,\n",
    "![](https://images.velog.io/images/moondeokjong/post/08252dd5-b284-41b6-bbed-b032a67fe73c/Screenshot%202022-02-16%20at%202.55.08%20PM.png)\n",
    "- $logp(Y∣X)$ 부분은 $\\mathbf{\\theta}$에 의한 식이 아니므로 제외하면\n",
    "![](https://images.velog.io/images/moondeokjong/post/2d2e4442-0ef9-43b1-890d-f7db758af9b2/Screenshot%202022-02-16%20at%202.55.11%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "junior-jefferson",
   "metadata": {},
   "source": [
    "- 우리가 최소화해야 할 posterior 함수를 편의상 $\\mathcal{P}(\\mathbf{\\theta})$로 놓으면(일반적인 notation 아님)\n",
    "![](https://images.velog.io/images/moondeokjong/post/6723142f-8453-4c61-bc1c-cc21658bc18c/Screenshot%202022-02-16%20at%202.57.48%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "painful-antenna",
   "metadata": {},
   "source": [
    "![](https://images.velog.io/images/moondeokjong/post/fb377d50-959d-41a3-824e-9993234a0503/Screenshot%202022-02-16%20at%202.58.31%20PM.png)\n",
    "![](https://images.velog.io/images/moondeokjong/post/71d03a79-01a5-418a-8815-3e23a28239a7/Screenshot%202022-02-16%20at%202.58.38%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "later-model",
   "metadata": {},
   "source": [
    "- MLE의 최적 파라미터 $\\mathbf{\\theta}_{ML} = (X^\\top X)^{-1}X^\\top\\mathbf{y}$와 비교하면, \n",
    "- 다른 점은 $(\\sigma^2/\\alpha^2)\\mathbf{I}$항이 더해졌다는 것. \n",
    "- 노이즈 분포의 분산 $\\sigma^2$과 파라미터 분포의 분산 $\\alpha^2$ 모두와 연결된 부분인데,\n",
    "- MLE와 MAP를 구분 지어주는 이 항이 어떤 의미를 가지고 있을까?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "equal-norwegian",
   "metadata": {},
   "source": [
    "### MAP as L2 regularization"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compatible-alfred",
   "metadata": {},
   "source": [
    "![](https://images.velog.io/images/moondeokjong/post/99e81b1f-e055-407e-a848-7b9d50116416/Screenshot%202022-02-16%20at%203.01.25%20PM.png)\n",
    "![](https://images.velog.io/images/moondeokjong/post/d0e1aa39-c6f2-47a3-a1e8-e5b4eaa7e027/Screenshot%202022-02-16%20at%203.01.31%20PM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "continuous-brother",
   "metadata": {},
   "source": [
    "## MLE와 MAP의 비교"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "determined-apple",
   "metadata": {},
   "source": [
    "### 데이터셋 생성"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "universal-blackjack",
   "metadata": {},
   "source": [
    "- MAP는 MLE와 비슷하지만 정규화 항에 해당하는 negative log prior 부분이 존재한다는 차이가 있었다. \n",
    "- 그래서 MLE 모델보다 MAP 모델이 더 안정적이라고 밝혔는데,\n",
    "- 이상치(outlier)가 있는 데이터셋을 이용해서 MAP와 MLE를 비교해 보도록 해보자."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "honey-harvey",
   "metadata": {},
   "source": [
    "- 이전 예제와 마찬가지로 y=x+1y=x+1 함수값에 랜덤한 노이즈를 더해서 데이터 포인트들을 생성.\n",
    "- 실험 결과 이상치 데이터 한 개를 데이터 포인트 20개에 추가하는 것으로는 모델에 큰 영향을 주지 못해서 데이터 포인트를 10개로 줄이고 이상치 데이터도 2개 추가\n",
    "- 그래프에서 $(0.5,9)$, $(1.5, 10)$ 위치의 이상치 데이터를 확인할 수 있다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "adaptive-intervention",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "np.random.seed(0)\n",
    "num_samples = 10\n",
    "\n",
    "input_data = np.linspace(-2, 2, num_samples)\n",
    "labels = input_data + 1 + np.random.normal(0, 0.5, size=num_samples)\n",
    "\n",
    "input_data = np.append(input_data, [0.5, 1.5])\n",
    "labels = np.append(labels, [9.0, 10.0])\n",
    "\n",
    "plt.scatter(input_data, labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "framed-disclaimer",
   "metadata": {},
   "source": [
    "### 파라미터 계산"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "accessible-institution",
   "metadata": {},
   "source": [
    "- MLE와 MAP의 최적 파라미터는 각각 다음과 같다.\n",
    "![](https://images.velog.io/images/moondeokjong/post/43ae834d-b738-4f82-8da8-ceb3149d9a5f/Screenshot%202022-02-16%20at%202.36.10%20PM.png)\n",
    "- 노이즈 분포의 표준편차 $\\sigma$는 0.1로 가정하고, 파라미터 분포의 표준편차 $\\alpha$는 0.04로 지정. \n",
    "- 정규화 상수 $\\lambda$가 $\\alpha^2$ 에 반비례하는 값. \n",
    "- $\\alpha$가 작을수록, 즉 파라미터 분포의 표준편차를 작게 잡을수록 파라미터 값에 대한 제약 조건을 강하게 걸어주는 것과 같다.\n",
    "- 정규화 측면에서 봐도 $\\lambda$ 값이 클수록 모델의 유연성은 감소."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "gorgeous-position",
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelihood(labels, preds):\n",
    "    result = 1/(np.sqrt(2*math.pi*0.1*0.1))*np.exp(-np.power(labels-preds,2)/(2*0.1*0.1))\n",
    "    \n",
    "    return np.prod(result)\n",
    "\n",
    "def neg_log_likelihood(labels, preds):\n",
    "    const_term = len(labels)*math.log(1/math.sqrt(2*math.pi*0.1*0.1))\n",
    "\n",
    "    return (-1)*(const_term + 1/(2*0.1*0.1)*np.sum(-np.power(labels-preds,2)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "personalized-adrian",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[MLE result] (blue)\n",
      "slope: 1.4748 bias: 2.4784\n",
      "likelihood: 0.0000e+00\n",
      "negative log likelihood: 4.1298e+03\n",
      "\n",
      "[MAP result] (orange)\n",
      "slope: 1.1719 bias: 1.6628\n",
      "likelihood: 0.0000e+00\n",
      "negative log likelihood: 4.6645e+03\n"
     ]
    },
    {
     "data": {
      "image/png": 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Sdb6FSq+P5z6s49LVHrIzU/nsHVPYVuZhWfHEkXcz8rouezc0HnGOT5gKi38rNJZ9n2u67MEUZWfgu0lYF2VHblMHBbhIjJ1pukpllY9Kr48zlzpIS0li4/x8Kso8rJmTR1rKCLsZ2XIuNJZ9Y5e9Esq+4AyN5M11ZZc9mMcfmHvdGDhARmoyjz8wN2LnUICLxMCl9m6er3EesvGea8EYuGdmDl9fN5vNiwoYP5K2H/N3w9l3+m9ANh11jk8ohiWfcwJ7xn2QPkKHhUL6xrmjOQvFWBu7TXKWL19u9+/fH7PzicRTZ0+A3YcvUun18caxRvxBy7yCcWwr8/BwaRGFEyK7P2JcNZ+9Ziz7Dei9CslpMO1eZ1hk9kbILRlxXXasGGMOWGuX33hcHbhIBAWClndPXmK718dLB+u42hOgYPwYvrJ6BhWlHuYXJtY85WHzd8PZt53APrEbmo45x7OnQenvhLrs1ZA2Cp4EjSMFuEiYrLUcqnVW/NtZXUtDWzfj0lPYsqSQilJnxb8Rsf1Y85nQ0499XXYHJKfD9Hvhji87nXbObHXZMaQAFxmmC80dH6/4d7yhndRkw9q5k9lW5mH9vMnuX/Gvt8vpsvvGsi8dd45PnA6l/8UJ7Omr1GXHkQJcZAhaO3o/3n5s35nLANw5fSJ/UbGIrUsKyc50+Yp/l0/3B/bpN8DfGeqyV8GdX3GGRnJmqctOEApwkVvo6g2w96iz/dhrRxrpCQSZlZfFdzfNobzUw9RJLt5+rLcLzr7VP5Z96YRzfOIMWPa7TmBPXwVpLv4aRzAFuMhNBIOWfWcuU+n18XxNHW1dfnLHpvO790xjW5mHhUUu3n7s8qn+wD79ptNlp4wJddlfDY1lz4p3lWGL9kJSiUABLnKNo/VtVFb52OH1UdvaRWZaMpsXFVBR6mHlrBxS3LjiX28nnHmrf/nVy6ec45NmwrLf6x/LTh050xpjsZBUIlCAy6hX39rFzmof2721HK67QnKS4b6SXP70U/PYuCCfzDQX/jO5dLI/sM+8Bf4uSMlwpvbd9TVnw94R0GUPJBYLSSUCF35nioSvrauXl0Ir/r1z8hLWwtKp2fzkoQVsXVpE7tj0eJc4ND0dTlD3rTHSfNo5njM7NMVvg/NQzQjqsgcTi4WkEoECXEaNHn+QN441UlnlY/dHF+n2B5mWk8k31pdQUeZhhpu2H7PW6bL7AvvMWxDoDnXZ98E9f+h02ZNmxLvSuIjFQlKJQAEuI5q1lg/O9a34V0tzRy+TstL47TunUl7qYVlxtntuRvZ0wJk3+4dGms84x3Nmh6b49XXZI3S98CGIxUJSiUABLiPSycZ2dnh9VFbVcu5yB+kpSWxaWMC2siJWl+S5Y/sxa51pfR+PZb/tdNmpmaEu+49GdZc9mFgsJJUIFOAyYjS2dfNsdS07qnxUX2jFGLh3Vi5/vN5Z8W+cG1b867nqTO3rGxppOescz50Dd/6BM5ZdvPKmXfZomDY3FBVlnhH/9SvAxdU6evy8fOgi270+3jrRRCBoWVg0nh88OJ+HlhZRMCHBhxOshabj/YF99p1ruuw1cO83nIdpJk4b9NOMlmlzcr1hB7gxZirwz0A+YIGnrbV/G6nCRAbiDwR5++QlKr0+dh2qp6MngCc7g8fum0lFmYc5+Qm+m0t3+/Vj2S3nnOO5c2HFV0Nj2Ssh5fZnwiTStDn9JBA74XTgfuA71toPjDHjgAPGmN3W2o8iVJvIx6y11PhaqfTWsrO6lqb2bsaPSaG81MO2Mg/Lp01M3BX/rIXGo/1d9rl3IdADqVkwcy2s+pYT2tnFwz5Fokyb008CsTXsALfW1gF1oddtxpjDgAdQgEvEnLvUwY4qH9urfJxqvEpachLr502moszDunl5pKck6Ip/3W3OYlB9y6+2nneO582Dux5zhkWK74GUyCx+lSjT5hLpJ4HRICJj4MaY6UAZ8P5NPvYo8ChAcfHwOwwZPZqv9vBcaMW/A2ebAbhrxiQeXT2TTy0qZEJmAt6MtBYaDjtd9ok9cPZdCPZC2lhnLHv1t53Qzp4aldMnyrS5RPlJYLQIO8CNMWOB/wC+aa29cuPHrbVPA0+Ds6VauOeTkamrN8Arh50V//YebcAftJRMHsv3Ns+lvNSDJxEfwOhug1N7Q132K3DlgnM8bz7c/bWId9mDSZRpc4nyk8BoEVaAG2NSccL7V9baZyJTkowWwaDlvdPOzcgXa+pp6/YzeVw6X753OuWlCbji37Vd9vHdcO69/i575lq477uhsezodNm3kgjT5hLlJ4HRIpxZKAb4B+CwtfavI1eSjHSH6/q3H6tr7WJsegqbFxWwrczZfiz5Nm9GxmS2Q9cVOP36J7vsyQvhnq87XfbUu2LSZbtBovwkMFoMe1d6Y8wq4E2gBgiGDn/fWvvCQH9Gu9KPXrUtneysdrYfO1LfRkqSYe3cPMpLPWyYn09G2tBuRt442wGcTu9nn14cXlhYCw0f9d98PPcuBP2QPh5mrnECe/YGmKBAktiJ+K701tq3gAT6+VYSTWtnLy8drGO718f7py9jLSwrzuan5QvZsqSISVnD71ojOtuhq/X6sey2Wud4/mJY+cdOYE+9C5IT8OapjGp6ElMiqtsfYO/RRiq9Pl450kCPP8jM3Cy+ef8cKsqKmJYTmRX/wprtYC1cPNjfZZ9//5oue62zwcHsDTC+KCK1ikSLAlyG7Max5+9smsPUSZls9/p4/sM6Wjt7yclK45EVxWwr87BkyoSI34wc8myHzhanyz7R12XXOcc/7rI3wtQV6rLFVRTgMiQ3e9LuO/9WjcUZg35gYT4VZR5Wzc6N6vZjt5ztYC3U14RmjIS6bBuA9Akwa23/WPb4wqjVKBJtCnAZkp+/eOQTY88WmJiZylt/up6s9Nh8S91stsP31xeyJW0fVO5xhkba6503FyyGe//EGRqZsgKS9W0vI4O+k+WW2rv9vHyonu1eH/VXum76npaO3piFd5+K0iIqCpr6x7Jf3Od02WMmwKz1oS77fhhXENO6RGJFAS431RsI8tbxJrZ7fbz8UT1dvUGmTMxgXHoKbd3+T7w/Zk/adTbDydecwD6xB9ovOscLlzqLQpVsBM9yddkyKui7XD5mraX6QiuVXh/PVtdy6WoPEzJS+cyyKWwr83DHtInsqKqN7ZN2wSDUf9g/ln1hH9ggjMl2uuySjTDrfhiXH53ziyQwBbhwpukqlVU+dlTVcrrpKmkpSWycn095aRFr504mLaX/ZmRMnrTruAwnXw112a/A1QbneGEprP6OMzTiuUNdtox6+hcwSl1q7+b5GuchG++5FoyBu2fk8F/XzGLz4gLGD7L9WMTX3AgGoa7KCezju8G33+myMyZeP5Y9dnLkzikyAijAR5HOngC7D1+k0uvjjWON+IOWeQXjeOJT8ygvLaJwQgxXjOvrso/vhpOvwNVG53hRGaz+bmgs+w5IStD1vkUSgAJ8hAsELe+evMR2r4+XDtZxtSdA4YQxfGX1DCpKPcwvHB+bQoJBqPM649gndoPvwDVd9v39Y9lj82JTj8gIoAAfgay1HKrtX/Gvoa2bcekpbFlSyLayKdw1Y1Jsth/ruOyMYffNGOloAozTZd/3eGgse5m6bJFhUoCPIBeaO9hR5az4d7yhndRkw7q5zvZj6+dNZkxqlIMyGIRab/962b4DgIXMnOvHsrNyo1uHyCihAHe51o5eng9tP7bvzGUA7pw+kb/ctogtiwvJzozyOtVXLzlj2H1j2R2XAOOMX699wgntolJ12SJRoAB3oW5/gNeOONuPvXakkZ5AkFl5WXx30xzKSz1MnZQZvZMHA06XfXx3aCz7A5wuO9dZW2T2RqfbzsqJXg0iAijAXSMYtOw7c5kdVc6Kf1e6/OSOTed375lGRamHRZ4obj/W3hialx1aya/zMmBgynJY+ySUbIDCMkiK3uJViSwmOwOJ3IQCPMEdu9jGdq+PHV4fta1dZKYls3lhARVlHlbOyonOin/BgDN+3ddl11bxcZddsik0Y2Q9ZE6K/Lld5marMz75TA2AQlyiTgGegOpbu9hZ7aPSW8tHdVdITjLcV5LLn35qHhsX5JOZFoW/tvbG0GyR3U633dkMJslZV2Td953hkcLSUdtlDySiOwOJDJECPEG0dfXy0sF6Kqt8vHPyEtZC6dRs/tvDC9mypJDcsemRPeEnumyvczwrD+ZsdgJbXfYthbUzkEiYFOBx1OMP8saxRrZX+djz0UW6/UGm5WTyjfUlVJR5mJEbme3HPtbe0P+4+slXoavF6bKn3AnrfuiMZRcsVZc9BEPeGUgkghTgMWat5YNzLVR6fTz3YS3NHb1Mykrjt++cSnmph2XF2ZG7GRnwO+uK9HXZddXO8azJMPdBJ7BnrlOXHYZb7gwkEkUK8Bg51dhOZeghm3OXO0hPSWLTwgK2lRWxuiSP1Nu8GXnLGQ9tF68fy+5qBZPs7Pe4/ofONL+CJeqyIyQmqzOKDMBYa2N2suXLl9v9+/fH7Hzx1tjWzXMfOqFdfaEVY2DlrBy2lU3hgYX5jBtkxb+buXHGA8DYVPj7NQHuM1VOp13/YegDBc44dskGZ6f1jImR+8JEJKaMMQestctvPK4OPMI6evy8fOgilVU+3jzeRCBoWVg0nh9umc9DS4vIHz9m2J+7b8bDZJpZk1zN2qQqVicdZPxbHaEu+y64/89CXfZiiNa8cBFJCArwCPAHgrx98hKVXh+7DtXT0RPAk53BY/fNpKLMw5z8ceGdIOCHC/t4pP2fWJtWzcKkswBctNm8GFjB68Gl/P2Pvg0Z2eF/MSLiGgrwYbLWUuNrpdJby87qWprauxk/JoXyUg8VpUXcOT3MFf+u1F0zlr0Xult5LCWJA8E5/FXv59kbXMphWwwYPNkZCm+RUUgBPkTnL3dQ6fWxvcrHqcarpCUnsX6es+Lfunl5pKcMc9GmQC+c39e/9+NF52k+xhXCgoehZCMvtc/l8WfP0BnQjAcRUYDfluarPTxXU8cOr4/9Z5sBWDFjEl9dPZMHFxUyIXNoNyM/dqW2f172qb3QfQWSUmDq3bDhJ85Ydv7Cj8eytwL+1HGa8SAiQJgBbozZDPwtkAz8wlr784hUlQC6egO8cthZ8e/1Yw30Bixz8sfyvc1zeXhpEVMmDmPFv0AvnHuvv8tuOOQcH1cECyucwJ65FsYMvEtOxPejFBHXGnaAG2OSgb8DNgIXgP80xuy01n4UqeJiLRi0vHfauRn5Yk09bd1+8sen86WV09lWNoX5heOG/pBNq69/g4NTr0NPGySlQvHdsPHPndCePF8zRkRkyMLpwFcAJ6y1pwCMMf8ClAMRDfBYLNV5uO4KlVU+dlbVUtfaxdj0FDYvKmBbmYe7Z+aQPJSbkf4eOP9e6OnHPdAQuhzjp8Diz4S67DWQHubMFBEZ9cIJcA9w/prfXwDuuvFNxphHgUcBiouLh3SCaC7VWdvSyc5q5yGbI/VtpCQZ1szJ48kH57Nxfj4ZaUO4Gdl6oT+wT+2Fnnany552D2z8qbP8at48ddkiElFRv4lprX0aeBqcJzGH8mcjvVTnla5eXqqpZ7vXx3unnRX/lhVn89PyhWxZUsSkrNvcfszfA+fe7R/LbjzsHB8/BRZ/Vl22iMREOAHuA6Ze8/spoWMRE4mlOnv8QfYebaCyyseeww30+IPMzM3iWxvmUF5axLSc21zxr+V8f2Cffv36Lrv0EWejg7y56rJFJGbCCfD/BEqMMTNwgvvzwCMRqSpkuEt1BoOWA+ea2e718UJNHS0dveRkpfHIimIqyjwsnTLh1jcj/d1Ol903NNJ4xDk+oRiWfM7psmfcB+ljh/vliYiEZdgBbq31G2P+CNiFM43wH621hyJWGUNfqvNEQxuV3loqq3xcaO5kTGoSD4S2H1s1O/fWK/41n72my34Deq9CchpMW0nN5If52fEpvHsxh6LuTB73zKVC4S0icRTWGLi19gXghQjV8gm3s1Rnw5UudlbXsqOqlhpfK0kGVpXk8e2Nc9i0sICx6YN8if5uOPu2E9gndkPTMed49jQo/Z1Ql72aykMt2vdQRBKOK5eTvdrtZ9ch52bk2yeaCFpY7JlARZmHh5YWMnncICv+NZ/pHxY5/Qb0dkByOky/1wnsko2QM/u6sex7f/7qTYdyPNkZvP3E+rC/HhGRwbh+OVl/IMibJ5qo9Pp4+dBFOnsDTJmYwdfXzqaizMPsyQMMZ/R2OV123yPrl447x7On9d98nL4K0ga+mal9D0UkEbkiwP969zF+9d5ZLl3tITszlU8v87CtzMMd0ybe/Gbk5dP9gX3mzeu77OW/f9MuezDa91BEEpErAvxqt5+7Z+ZQUeZhzZw80lJuuBnZ2wVn3+ofy750wjk+cQaUfcHZmWb6akgbxvolaN9DEUlMrgjwH21d8MmDl0/1B/bpN8HfCSljnOGQO7/qhHbu7IicX/seikgickWAA9DbCWfe7l8Y6vJJ5/ikmbDs95xhkWn3DrvLvhWtAigiicYdAf7ct6Dq19d02avhrsecLjtnVryrExGJC3cE+ISpcMcXnWl+0++FVN08FBFxR4Cv/na8KxARSTi3eLZcREQSlQJcRMSlFOAiIi6lABcRcSkFuIiISynARURcSgEuIuJSCnAREZeK6YYOxphG4Oww/3gu0BTBciJFdQ2N6hoa1TU0I7WuadbavBsPxjTAw2GM2X+zHSniTXUNjeoaGtU1NKOtLg2hiIi4lAJcRMSl3BTgT8e7gAGorqFRXUOjuoZmVNXlmjFwERG5nps6cBERuYYCXETEpRI2wI0xTxljjhhjPjTGbDfGZA/wvs3GmKPGmBPGmCdiUNdvGWMOGWOCxpgBpwUZY84YY2qMMVXGmP0JVFesr9ckY8xuY8zx0H8nDvC+QOhaVRljdkaxnkG/fmNMujHmX0Mff98YMz1atQyxri8ZYxqvuUZ/EKO6/tEY02CMOTjAx40x5n+G6v7QGLMsAWpaa4xpveZa/Vm0awqdd6ox5jVjzEehf4t/cpP3RPZ6WWsT8hewCUgJvf4r4K9u8p5k4CQwE0gDqoEFUa5rPjAX2AssH+R9Z4DcGF6vW9YVp+v134EnQq+fuNnfY+hj7TG4Rrf8+oGvA/8n9PrzwL8mSF1fAv5XrL6frjnvfcAy4OAAH38QeBEwwN3A+wlQ01rguThcq0JgWej1OODYTf4eI3q9ErYDt9a+bK31h377HjDlJm9bAZyw1p6y1vYA/wKUR7muw9bao9E8x3DcZl0xv16hz//L0OtfAhVRPt9gbufrv7be3wD3G2NMAtQVF9baN4DLg7ylHPhn63gPyDbGFMa5priw1tZZaz8IvW4DDgOeG94W0euVsAF+g9/H+b/WjTzA+Wt+f4FPXrB4scDLxpgDxphH411MSDyuV761ti70uh7IH+B9Y4wx+40x7xljKqJUy+18/R+/J9RAtAI5UapnKHUBfCb0Y/dvjDFTo1zT7UrUf4P3GGOqjTEvGmMWxvrkoaG3MuD9Gz4U0esV102NjTF7gIKbfOgH1todoff8APADv0qkum7DKmutzxgzGdhtjDkS6hziXVfEDVbXtb+x1lpjzEDzVqeFrtdM4FVjTI219mSka3WxZ4FfW2u7jTGP4fyUsD7ONSWqD3C+n9qNMQ8ClUBJrE5ujBkL/AfwTWvtlWieK64Bbq3dMNjHjTFfArYC99vQANINfMC1nciU0LGo1nWbn8MX+m+DMWY7zo/JYQV4BOqK+fUyxlw0xhRaa+tCPyo2DPA5+q7XKWPMXpzuJdIBfjtff997LhhjUoAJwKUI1zHkuqy119bwC5x7C4kgKt9T4bg2NK21Lxhj/t4Yk2utjfoiV8aYVJzw/pW19pmbvCWi1ythh1CMMZuB7wEPW2s7BnjbfwIlxpgZxpg0nJtOUZvBcLuMMVnGmHF9r3FuyN70jnmMxeN67QS+GHr9ReATPykYYyYaY9JDr3OBe4GPolDL7Xz919b7WeDVAZqHmNZ1wzjpwzjjq4lgJ/B7odkVdwOt1wyZxYUxpqDvvoUxZgVOzkX7f8KEzvkPwGFr7V8P8LbIXq9Y36kdwh3dEzhjRVWhX30zA4qAF264q3sMp1v7QQzq2oYzbtUNXAR23VgXzmyC6tCvQ4lSV5yuVw7wCnAc2ANMCh1fDvwi9HolUBO6XjXAV6JYzye+fuDPcRoFgDHAv4e+//YBM6N9jW6zrp+FvpeqgdeAeTGq69dAHdAb+v76CvA14Guhjxvg70J11zDIzKwY1vRH11yr94CVMbpWq3DufX14TW49GM3rpUfpRURcKmGHUEREZHAKcBERl1KAi4i4lAJcRMSlFOAiIi6lABcRcSkFuIiIS/1/ddjsU6wwsP0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# X: 21x2 matrix, y: 21x1 matrix\n",
    "# input_data 리스트를 column vector로 바꾼 다음 np.append 함수로 상수항을 추가합니다.\n",
    "X = np.append(input_data.reshape((-1, 1)), np.ones((num_samples+2, 1)), axis=1)\n",
    "y = labels\n",
    "\n",
    "# MLE 파라미터 계산식\n",
    "mle_theta_1, mle_theta_0 = np.dot(np.dot(np.linalg.inv(np.dot(X.T, X)), X.T), y)\n",
    "# MAP 파라미터 계산식\n",
    "map_theta_1, map_theta_0 = np.dot(np.dot(np.linalg.inv(np.dot(X.T, X)+(0.1*0.1)/(0.04*0.04)*np.eye(2)), X.T), y)\n",
    "\n",
    "print('[MLE result] (blue)')\n",
    "print('slope: '+'%.4f'%mle_theta_1+' bias: '+'%.4f'%mle_theta_0)\n",
    "\n",
    "mle_preds = mle_theta_1 * input_data + mle_theta_0\n",
    "print('likelihood: '+'%.4e'%likelihood(labels, mle_preds))\n",
    "print('negative log likelihood: '+'%.4e\\n'%neg_log_likelihood(labels, mle_preds))\n",
    "\n",
    "print('[MAP result] (orange)')\n",
    "print('slope: '+'%.4f'%map_theta_1+' bias: '+'%.4f'%map_theta_0)\n",
    "\n",
    "map_preds = map_theta_1 * input_data + map_theta_0\n",
    "print('likelihood: '+'%.4e'%likelihood(labels, map_preds))\n",
    "print('negative log likelihood: '+'%.4e'%neg_log_likelihood(labels, map_preds))\n",
    "\n",
    "model_x = np.linspace(-2, 2, 50)\n",
    "mle_model_y = mle_theta_1 * model_x + mle_theta_0\n",
    "map_model_y = map_theta_1 * model_x + map_theta_0\n",
    "\n",
    "plt.scatter(input_data, labels)\n",
    "plt.plot(model_x, mle_model_y)\n",
    "plt.plot(model_x, map_model_y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "auburn-admission",
   "metadata": {},
   "source": [
    "- 위 그래프에서 파란색 직선과 주황색 직선은 각각 MLE, MAP를 이용해 찾은 모델을 나타낸다.\n",
    "- 파란색 직선은 이상치 데이터까지 포함한 negative log likelihood를 감소시키기 위해 직선이 위로 치우쳐서 아래쪽 10개 데이터의 경향성에서는 약간 벗어났다. \n",
    "- 반면 주황색 직선은 이상치 데이터가 추가되어도 아래쪽 데이터에서 크게 벗어나지는 않고 있다.\n",
    "- 원래 데이터 분포에서 멀리 떨어진 이상치 데이터가 추가되었기 때문에, likelihood의 값은 언더플로우가 발생해서 0으로 표시됨\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "chronic-hawaiian",
   "metadata": {},
   "source": [
    "- negative log likelihood의 값을 보면 MLE 결과와 MAP 결과를 비교할 수 있다. \n",
    "- MAP가 MLE에 비해 negative log likelihood 값이 크지만(likelihood가 작지만), 이상치 데이터가 추가되었을 때 모델 파라미터의 변화는 MLE보다 작다."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}